One of the most difficult operations in a machine shop is that of machining flat faces on thin discs such as those used in automotive brakes. In the case of brake discs, for example, it was a common practice to subject the faces of the discs to a grinding operation to provide the relatively flat surfaces required to meet manufacturer's specifications and to provide good braking. More recently, such a grinding operation has in many cases been replaced by a machining operation carried out with the aid of a vibration dampener such as that described in U.S. Pat. No. 3,691,878. Although that vibration dampener is satisfactory for many operations, it has its limitations. For example, attempts to resurface very thin stainless steel discs have not been entirely successful since some noticable vibration or chatter is present and causes an irregularity in the disc surfaces. There is, therefore, a need for an improved vibration dampener which may be adapted for use with thin brake discs during machining of the surfaces thereof.